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Re: A simplification challenge.

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On 12.09.2014 22:29, peter.luschny@gmail.com wrote:
>>> bi:=n->BesselI(4+n,-2); bk:=n->BesselK(4+n,2);
>>> i:=n->BesselI(n,2); k:=n->BesselK(n,2);
>>> Simplify
>>> a := n ->(bi(n)*(5*k(5)-k(6))+bk(n)*(5*i(5)+i(6)))/(i(6)*k(5)+i(5)*k(6));
 >>
>> Hm ... http://oeis.org/A058309 due to your hint: using the package 'gfun'
>> finds a recursion rec := {-u(n)+(-n-5)*u(n+1)+u(n+2), u(0)=0, u(1)=1},
>> feeding a for u and calling 'simplify' confirms it.
>
> Nice idea! And indeed the recursion is the name of the sequence :-)
> But much more is true.
>
> However what I really wanted to find is something different:
> a hypergeometric representation. There exists a simple one
> but Maple apparently does not know how to derive it.

Yes (if you have the solution from the paper already typed in
then please post it).

I tried code from http://www.math.fsu.edu/~hoeij/papers.html
as well (bottom ---> Giles Levy (*)), but for your task that
does not work for me (even if NOT starting in 0, but in 1).

(*) http://www.math.fsu.edu/~glevy/implementation/

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Thread

A simplification challenge. peter.luschny@gmail.com - 2014-09-11 10:53 -0700
  Re: A simplification challenge. Axel Vogt <&noreply@axelvogt.de> - 2014-09-12 19:30 +0200
    Re: A simplification challenge. peter.luschny@gmail.com - 2014-09-12 13:29 -0700
      Re: A simplification challenge. Axel Vogt <&noreply@axelvogt.de> - 2014-09-12 22:50 +0200
        Re: A simplification challenge. peter.luschny@gmail.com - 2014-09-13 11:46 -0700
          Re: A simplification challenge. Axel Vogt <&noreply@axelvogt.de> - 2014-09-13 22:06 +0200

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